{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:76HYUZ3K34ZE2PFPBUA4GKWWQU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"eecf7add09f2f15a9d8ce6e70a3054cf8e6a515f8670199b93a85f5efc1d7c46","cross_cats_sorted":["astro-ph.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.IM","submitted_at":"2026-07-07T03:28:08Z","title_canon_sha256":"c6e0b4bf8b7fe3bae91dfaf7c4d881bbe6a28ac77f6f95aef4c4a7ba35de9efa"},"schema_version":"1.0","source":{"id":"2607.06604","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06604","created_at":"2026-07-09T00:19:19Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06604v1","created_at":"2026-07-09T00:19:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06604","created_at":"2026-07-09T00:19:19Z"},{"alias_kind":"pith_short_12","alias_value":"76HYUZ3K34ZE","created_at":"2026-07-09T00:19:19Z"},{"alias_kind":"pith_short_16","alias_value":"76HYUZ3K34ZE2PFP","created_at":"2026-07-09T00:19:19Z"},{"alias_kind":"pith_short_8","alias_value":"76HYUZ3K","created_at":"2026-07-09T00:19:19Z"}],"graph_snapshots":[{"event_id":"sha256:74eda20bba0153c14b65ce9983c48f610ddf01b3ab381c2635f39b5618e09e89","target":"graph","created_at":"2026-07-09T00:19:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.06604/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a significant update to GRAMSCI (GRAph Made Statistics for Cosmological Information; Sabiu et.al 2019), an algorithm for the fast computation of the general $N$-point spatial correlation function of any discrete point set embedded in $\\mathbb{R}^n$. Utilizing the concepts of kd-trees and graph databases, we count all possible $N$-tuples in binned configurations within a given length scale.\n  In this {\\em Version 2 update} we describe several additions to the original code. We replace the binary-search inner loop, which cost $O(m\\log m)$ per hub--spoke pair, where $m$ is the mean nei","authors_text":"Cristiano G. Sabiu","cross_cats":["astro-ph.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.IM","submitted_at":"2026-07-07T03:28:08Z","title":"Fast Graph-based Higher-Order Clustering Statistics on the GPU"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06604","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:85cba34a5ac7ca74578a322d59e2e42551174e94d68b62350e7113e66bd4a693","target":"record","created_at":"2026-07-09T00:19:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"eecf7add09f2f15a9d8ce6e70a3054cf8e6a515f8670199b93a85f5efc1d7c46","cross_cats_sorted":["astro-ph.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.IM","submitted_at":"2026-07-07T03:28:08Z","title_canon_sha256":"c6e0b4bf8b7fe3bae91dfaf7c4d881bbe6a28ac77f6f95aef4c4a7ba35de9efa"},"schema_version":"1.0","source":{"id":"2607.06604","kind":"arxiv","version":1}},"canonical_sha256":"ff8f8a676adf324d3caf0d01c32ad6850a1f49b468206e33b02c21e95808932c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff8f8a676adf324d3caf0d01c32ad6850a1f49b468206e33b02c21e95808932c","first_computed_at":"2026-07-09T00:19:19.998502Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T00:19:19.998502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AHsobzWiJEy/MDj5G9HMW4J38W6Im4pFu7YZ+etgdUy88VJVy0UDI/eUDxqtVAWunWEES8PnIHUQDBw4mn2MCQ==","signature_status":"signed_v1","signed_at":"2026-07-09T00:19:19.999185Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06604","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85cba34a5ac7ca74578a322d59e2e42551174e94d68b62350e7113e66bd4a693","sha256:74eda20bba0153c14b65ce9983c48f610ddf01b3ab381c2635f39b5618e09e89"],"state_sha256":"aef32bdfee355280afa5a2ea9878957262643d7e16dd89aebc24b7b27c7d1ed3"}